Precision in estimating Unruh temperature

Abstract

The goal of quantum metrology is the exploitation of quantum resources, like entanglement or quantum coherence, in the fundamental task of parameter estimation. Here we consider the question of the estimation of the Unruh temperature in the scenario of relativistic quantum metrology. Specifically, we study two distinct cases. First, a single Unruh-DeWitt detector interacting with a scalar quantum field undergoes an uniform acceleration for a finite amount of proper time, and the role of coherence in the estimation process is analyzed. After this, we consider two initially entangled detectors, one of which is inertial while the other one undergoes acceleration. Our results show that the maximum of the Fisher information, thus characterizing the maximum possible precision according to Crammér-Rao bound, occurs only for small accelerations, while it decreases fast when acceleration increases. Moreover, the role of initial coherence ---in the single detector case---, or entanglement ---in the two detectors case---, is to decrease Fisher information. Therefore, under the considered protocol, internal coherence (or entanglement) is not a resource for estimating Unruh temperature. These unexpected results show that a detection of the Unruh effect can be even more challenge than previously thought. Finally, by considering the connection between Unruh effect and Hawking radiation, we discuss how our results can be understood in the context of the estimation of Hawking temperature.

References in corpus (24)

• Advances in Quantum Metrology
• Quantum-enhanced measurements: beating the standard quantum limit
• The Unruh effect and its applications
• Alice falls into a black hole: Entanglement in non-inertial frames
• Microwave Quantum Illumination
• Quantum Illumination at the Microwave Wavelengths
• Entanglement of Dirac fields in non-inertial frames
• Quantum Entanglement of Moving Bodies
• Generalized Geometric Quantum Speed Limits
• Thermometry in the quantum regime: Recent theoretical progress
• Sudden death of entanglement and teleportation fidelity loss via the Unruh effect
• Relativity and Lorentz Invariance of Entanglement Distillability
• Sudden change in quantum and classical correlations and the Unruh effect
• Boundary conditions in the Unruh problem
• Bridging thermodynamics and metrology in non-equilibrium Quantum Thermometry
• Relativistic Quantum Metrology in Open System Dynamics
• Proposal for observing the Unruh effect with classical electrodynamics
• Quantum metrology and estimation of Unruh effect
• Coherent measurements in quantum metrology
• Spin and localization of relativistic fermions and uncertainty relations
• Macroscopic aspects of the Unruh effect
• Quantum interactions between a laser interferometer and gravitational waves
• Influence of detector motion in Bell inequalities with entangled fermions
• Influence of detector motion in entanglement measurements with photons